As an invesment Mrs. Astor purchased 2 paintings. She later sold the two paintings for $24,000 each. On one painting she made a 20% profit, but on the other she esperienced a 20% loss. Mrs. Astor lost__________ on her investments in the 2 paintings.
Purchase price of first :
1.2x = 24000
x = 24000/1.2 = 20,000
purchase price of 2nd:
.8y = 24000
y = 24000/.8 = 30,000
total purchase price = 50,000
total selling price = 48.000
loss on investment = 50000-48000 = 2,000
check:
on first:
profit = 4000
percentage profit = 4000/20000 = .2 or 20%
on 2nd:
loss = 6000
percentage loss = 6000/3000 = .2 or 20%
To determine the loss Mrs. Astor experienced on her investments in the two paintings, we need to calculate the net profit/loss on each painting individually.
Let's start with the first painting, where she made a 20% profit. To find the profit amount, we can multiply the purchase price of the painting by 20% (or 0.2), and then add this profit to the original purchase price.
Profit on the first painting = 20% of purchase price of the first painting + purchase price of the first painting
Similarly, for the second painting, where Mrs. Astor experienced a 20% loss, we can calculate the loss amount in the same way. We'll multiply the purchase price of the second painting by 20% (or 0.2), and then subtract this loss from the original purchase price.
Loss on the second painting = 20% of purchase price of the second painting - purchase price of the second painting
Next, we need to calculate the total profit/loss by adding the individual profit and loss amounts.
Total profit/loss = profit on the first painting + loss on the second painting
Finally, we can subtract the total profit/loss from the total selling price of the two paintings to find the amount Mrs. Astor lost.
Loss = Total selling price - total profit/loss
Let's calculate the loss:
Profit on the first painting = 20% of purchase price of the first painting + purchase price of the first painting
Loss on the second painting = 20% of purchase price of the second painting - purchase price of the second painting
Total profit/loss = profit on the first painting + loss on the second painting
Loss = Total selling price - total profit/loss
Plug in the values for the purchase price and selling price to find the answer.